Diffusion coefficient of a Brownian particle in equilibrium and nonequilibrium: Einstein model and beyond

TL;DR

This paper reviews the temperature dependence of the diffusion coefficient for Brownian particles modeled by Langevin dynamics, covering equilibrium and nonequilibrium cases, including periodically driven systems with non-monotonic behavior.

Contribution

It provides a comprehensive survey of diffusion coefficients in various physical models, extending Einstein's theory to nonequilibrium and driven systems.

Findings

Diffusion coefficient follows Einstein's theory in equilibrium.

Non-monotonic temperature dependence observed in driven nonequilibrium systems.

Survey includes models with periodic potentials and time-dependent driving.

Abstract

Diffusion of small particles is omnipresent in a plentiful number of processes occurring in Nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow down our survey for the case of the diffusion coefficient for a Brownian particle which can be modeled in the framework of Langevin dynamics. Our main focus will center on the temperature dependence of the diffusion coefficient for several fundamental models of diverse physical systems. Starting out with diffusion in equilibrium for which the Einstein theory holds we consider a number of physical situations away from free Brownian motion and end with surveying nonequilibrium diffusion for a time-periodically driven Brownian particle dwelling randomly in a periodic potential. For this latter situation the diffusion coefficient exhibits an intriguingly non-monotonic dependence on temperature.